Impact of dielectric environment and pressure on the ionization potential, electron affinity, and surface plasmon resonance of metal cluster

In the framework of the density functional method and the elastic stabilized jellium model, an analytical theory of size corrections for large self-compressed charged metallic clusters of radius R embedded in a dielectric matrix with permittivity ɛ is developed. We introduce the cluster shrinkage as a result of the action of surface forces. From the condition of mechanical equilibrium, using inverse radius 1/R expansion, an exact analytical expression for the first size correction to the electron chemical potential is derived. The problem of finding the first size corrections is reduced to solving the problem for a flat surface. The ionization potential is defined as the sum of the electron chemical potential for a neutral cluster, depending on R and ɛ, as well as the ordinary electrostatic contribution e2/(2ɛR). Using the analytic expressions derived, the term connected with spontaneous deformation has been estimated. The calculations show noticeable size-shrinkage contributions to the electron density, ionization potential, electron affinity, and surface plasma resonance. Additionally, we investigated the effects of external hydrostatic pressure on the surface characteristics of the cluster. The reasons for the alternating size shift in the energy of surface plasmons of charged metal particles embedded in a dielectric matrix observed in experiments are discussed.